Publications [#302440] of Heekyoung Hahn

Papers Published

1. Hahn, H, On zeros of Eisenstein series for genus zero Fuchsian groups, Proceedings of the American Mathematical Society, vol. 135 no. 8 (August, 2007), pp. 2391-2401, American Mathematical Society (AMS), ISSN 0002-9939
   (last updated on 2024/04/24)

   Abstract:
   Let Γ ≤ SL2(ℝ) be a genus zero Fuchsian group of the first kind with ∞ as a cusp, and let EΓ2k be the holomorphic Eisenstein series of weight 2k on Γ that is nonvanishing at ∞ and vanishes at all the other cusps (provided that such an Eisenstein series exists). Under certain assumptions on Γ, and on a choice of a fundamental domain F, we prove that all but possibly c(Γ, F) of the nontrivial zeros of EGamma;2k lie on a certain subset of {z ∈ h: jΓ(z) ∈ℝ}. Here c(Γ, F) is a constant that does not depend on the weight, h is the upper half-plane, and jΓ is the canonical hauptmodul for Γ. © 2007 American Mathematical Society Reverts to public domain 28 years from publication.